Stable Sets in Three Agent Pillage Games

Department of Economics Discussion Paper, University of Birmingham, 09-07

29 Pages Posted: 21 Jul 2009

See all articles by Manfred Kerber

Manfred Kerber

University of Birmingham - School of Computer Science

Colin Rowat

University of Birmingham - Department of Economics

Date Written: June 30, 2009

Abstract

Jordan [2006, “Pillage and property”, JET] characterises stable sets for three special cases of ‘pillage games’. For anonymous, three agent pillage games we show that: when the core is non-empty, it must take one of five forms; all such pillage games with an empty core represent the same dominance relation; when a stable set exists, and the game also satisfies a continuity and a responsiveness assumption, it is unique and contains no more than 15 elements. This result uses a three step procedure: first, if a single agent can defend all of the resources against the other two, these allocations belong to the stable set; dominance is then transitive on the loci of allocations on which the most powerful agent can, with any ally, dominate the third, adding the maximal elements of this set to the stable set; finally, if any allocations remain undominated or not included, the game over the remaining allocations is equivalent to the ‘majority pillage game’, which has a unique stable set [Jordan and Obadia, 2004, “Stable sets in majority pillage games”, mimeo].

Non-existence always reflects conditions on the loci of allocations along which the most powerful agent needs an ally. The analysis unifies the results in Jordan [2006] when n = 3.

Keywords: pillage, cooperative game theory, core, stable sets, algorithm

JEL Classification: C63, C71, P14

Suggested Citation

Kerber, Manfred and Rowat, Colin, Stable Sets in Three Agent Pillage Games (June 30, 2009). Department of Economics Discussion Paper, University of Birmingham, 09-07. Available at SSRN: https://ssrn.com/abstract=1429326 or http://dx.doi.org/10.2139/ssrn.1429326

Manfred Kerber

University of Birmingham - School of Computer Science ( email )

Edgbaston
Edgbaston, Birmingham B15 2TT B17 0JH
United Kingdom

Colin Rowat (Contact Author)

University of Birmingham - Department of Economics ( email )

Economics Department
Birmingham, B15 2TT
United Kingdom
+44 121 414 3754 (Phone)
+44 121 414 7377 (Fax)

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